Finally, DQMC has been applied to the square lattice away from half filling [1]}, [2]}, [3]}, [4]}. These calculations require massive computing resources, and have currently been performed for systems for size \(L=8\)  at temperatures down to \(T/t \simeq 0.2\)  and interaction strength \(U/t = 8\) . At these temperatures, finite size effects are found to be small, such that \(L=8\)  is probably sufficient
to make inferences about the thermodynamic limit. No symmetry broken phase was found. However, there are significant short-range correlations [1]} indicative of incommensurate unidirectional spin density wave,
\(d\) -wave superconductivity, as well as nematic bond order [4]}, that grow as the temperature decreases.
